MHB Find Integer Solutions for (A+3B)(5B+7C)(9C+11A)=1357911

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The equation (A+3B)(5B+7C)(9C+11A)=1357911 requires finding integer solutions by first determining the prime factors of 1357911, which are five in total. The next step involves forming all possible groups of three factors from these prime factors to explore potential combinations. Participants in the discussion suggest using systematic approaches to test various integer values for A, B, and C. The complexity of the equation indicates that solutions may be limited or require extensive computation. Overall, the focus remains on identifying viable integer combinations that satisfy the equation.
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Find all integer solutions (if any) for the equation $(A+3B)(5B+7C)(9C+11A)=1357911$.
 
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I would start by finding the prime factors of 1375911 (there are five) then forming all groups of 3 factors.
 
Hi HallsofIvy!

Thanks for your reply. But since this is a challenge question, I hope you know our expectation here is to receive a full solution, no more, no less. (Happy)
 
No solution because

RHS is odd so all factors are odd so each term in the LHS is odd. there are 3 terms on the LHS and so their sum has to be odd.

but sum is 12A + 8B + 16C which is even so impossible
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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